Improved Modeling of Microwave Structures Using Performance-Driven Fully-Connected Regression Surrogate

Abstract

Fast replacement models (or surrogates) have been widely applied in the recent years to accelerate simulation-driven design procedures in microwave engineering. The fundamental reason is a considerable-and often prohibitive-CPU cost of massive full-wave electromagnetic (EM) analyses related to solving common tasks such as parametric optimization or uncertainty quantification. The most popular class of surrogates are data-driven models, which are fast to evaluate, versatile, and easy to handle. Notwithstanding, the curse of dimensionality as well as the utility demands (e.g., so that the model covers sufficiently broad ranges of the system operating conditions), limit the applicability of conventional methods. A performance-driven modeling paradigm allows for mitigating these issue by focusing the surrogate setup process in a constrained domain encapsulating designs being of high quality w.r.t. the assumed figures of interest. The nested kriging framework capitalizing on this idea, renders the constrained surrogate using kriging interpolation, and has been shown to surpass traditional approaches. In pursuit of further accuracy improvements, this work incorporates the performance-driven concept into the fully-connected regression model (FRCM). The latter has been recently introduced in the context of frequency selective surfaces, and combined deep neural networks with Bayesian optimization, the latter employed to determine the network architecture and hyper-parameters. Using two examples of miniaturized microstrip couplers, our methodology is demonstrated to outperform both conventional modeling techniques and nested kriging, with reliable models constructed over multi-dimensional parameters spaces using just a few hundreds of samples.INDEX TERMS Dara-driven modeling; surrogate modeling; performance-driven surrogates; nested kriging; deep regression model; Bayesian optimization.

Design Centering of Compact Microwave Components Using Response Features and Trust Regions

“…x (17) where x (i) , i = 0, 1, …, are approximations to the optimum design x*. The yield estimated in the ith iteration, Ys (i) , is computed based on the surrogate model established in the current domain being the interval [x (i) -dl, x (i) -dl], with x (i) = [x1 (i) … xn (i) ] T , i.e., the domain is always centred at the current iteration point.…”

“…Undeniably, the most widespread approaches today are surrogate-assisted methods, where statistical analysis or yield optimization are carried out using a fast replacement model (e.g., neural networks [12], response surface approximation [13], polynomial chaos expansion, PCE [14][15][16]). A practical limitation is the dimensionality of the parameter space, i.e., the number of training data samples (translating into a computational cost of its acquisition) required for a construction of a reliable surrogate quickly increases with the number of the circuit parameters (also called the curse of dimensionality [17]). Available mitigation techniques include diminishing a number of directly handled dimensions [18], the usage of advanced modeling techniques (e.g., PC kriging, in which traditional trend functions, such as polynomials of low order, are substituted with PCE [19]), incorporation of model order reduction [20], as well as variable-resolution methods (co-kriging [21], space mapping [22]).…”

Reduced-cost two-level surrogate antenna modeling using domain confinement and response features

“…As a matter of fact, the list of advantages of data-driven surrogates is considerably longer: low evaluation cost, flexibility, no need for physical insight into the system under design, and transferability between various application areas. Some of widely used techniques of this class include kriging 35 , 36 , radial basis functions (RBF) 37 , Gaussian process regression (GPR) 38 , support vector regression 39 , and neural networks in many variations 40 , 41 . Still, a construction of data-driven surrogates for modern antennas featuring intricate topologies and large numbers of geometry parameters is challenging.…”

Surrogate‐assisted optimization of 3D printed ceramic nonuniform nonplanar microstrip filter

“…[3][4][5][6] Datadriven surrogate models are based on approximating sampled data which allow the model to make a prediction of targeted output characteristics using the given inputs without the need of expert knowledge of the selected problem, high adaptation rate between similar problems, and high computational efficiency. 6,7 Modeling and development of data-driven models is a topic that being studied by many researchers. Some examples of the commonly used modeling methods for microwave applications from literature can be named as kriging, 8 neural networks, [9][10][11][12] support vector regression, [13][14][15] and deep learning.…”

“…Some examples of the commonly used modeling methods for microwave applications from literature can be named as kriging, 8 neural networks, [9][10][11][12] support vector regression, [13][14][15] and deep learning. 6,7,[16][17][18][19][20][21] Although the utilization of data-driven surrogate models is a viable technique for design and optimization of microwave components, these methods are also has challenging design problems which must be addressed with care. (I) Properly creating data set, either using three-dimensional (3D) EM simulation or experiential data, for model is one of the most crucial step.…”